Getting to a file easily/quickly in blender's file browser
Blender's file selector doesn't support this kind of filtering, but since you ask this question, here is some related functionality.


You can use Tab to auto-complete when typing a file name as you would in a shell..
You can also filter files by typing wildcards into the filename field *. followed by an extension eg foo*.blend, project*.*. When you press Enter, this will highlight all files with the extension in the current directory. (you can use A to clear the highlighting).
When opening files, you can use the filters available in the header to help narrow your search etc.. 




Search (Addon)

There is an addon that can further help you when searching for files called File Browser Search. It presents you with a list of results that matched your query.